Publication: On wsq-primary ideals
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Date
2023-01-01
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Abstract
We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$. The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0\neq ab\in Q$ for some $a,b\in R$, then $a^2\in Q$ or $b\in\sqrt{Q}.$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.
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Temel Bilimler, Natural Sciences, Temel Bilimler (SCI), Doğa Bilimleri Genel, ÇOK DİSİPLİNLİ BİLİMLER, Natural Sciences (SCI), NATURAL SCIENCES, GENERAL, MULTIDISCIPLINARY SCIENCES, Multidisipliner, Multidisciplinary, primary ideal, weakly primary ideal, quasi-primary ideal, weakly 2-prime ideal, strongly quasi-primary ideal
Citation
Aslankarayiğit Uğurlu E., Tekir Ü., Koç S., "On wsq-primary ideals", CZECHOSLOVAK MATHEMATICAL JOURNAL, sa.1, ss.1-15, 2023